具有相关索赔风险模型的破产概率

本文考虑了具有两类索赔的风险模型,这两类索赔的计数过程是相关的Poisson过程和Erlang过程.通过Laplace变换方法,得到了该风险模型在索赔额为任意分布情形下破产概率的计算公式,并在索赔额为指数分布的情形下,得到了破产概率的精确表达式.     

索赔次数为复合Poisson-Geometric过程的风险模型及破产概率

本文引入一类复合Poisson-Geometric分布,这类分布包括两个参数,是普通Poisson分布的一种推广,并在保险中有其实际的应用背景;基于此分布产生一个计数过程,称之为复合Poisson-Geometric过程.本文着重研究了索赔次数为复合Poisson-Geometric过程的风险模型,这种模型是经典风险模型的一个推广.针对此模型,本文给出了破产概率公式及更新方程.作为特例,当索赔额服从指数分布时,给出了破产概率的显式表达式.     

带干扰的复合负二项过程下的双险种负风险模型

本文研究了带干扰的索赔过程为复合负二项过程的双险种负风险和模型.用两种不同的方法得到了该模型的最终破产概率,还得到了Lundberg不等式,推广了经典负风险模型.     

相关风险和模型的破产概率

本文研究了两险种理赔到达过程相关的正风险和模型与负风险和模型.利用Lundberg指数是相关因子的单调递减函数的性质,证明了破产概率是随着相关因子的增加而增大的,从而将相应的结果推广到了两险种理赔到达过程相关的风险和模型.     

依生灭过程索赔两险种风险模型

本文建立了依生灭过程索赔的两险种风险模型,主要对该模型的破产概率进行了研究,并给出了关于条件破产概率序列的微分积分方程以及破产概率收敛速率的上界,这类似于Cramer-Lundberg逼近,其逼近程度虽然不如Cramer-Lundberg逼近"精确",但不要求索赔额分布是尾指数的.     

一类推广负风险和模型的破产概率

本文研究了带干扰的两险种负风险和模型的破产问题.利用无穷小方法,给出了该风险模型破产概率所满足的微分-积分方程,并推导出破产概率满足的Lundberg型不等式.最后指出了当索赔服从负指数分布时破产概率的上界,推广了经典风险模型的结果.     

竞争型二元风险模型破产概率

本文研究了竞争型的二元风险模型,定义了两类破产概率以及状态过程,利用经典风险模型的已有结果和条件期望的性质,得到两类破产概率表达式,以及单个保险公司有限时间破产概率和最终破产概率,并给出两个保险公司的状态过程的概率分布列.     

一类相依两险种风险模型的分类破产概率

本文考虑文[1]中引入的一类索赔达到计数过程相关的两险种风险模型.利用更新方法,获得了该风险模型的分类破产概率的渐进结果,并给出了指数索赔情形下分类破产概率的表达式,从而改进了文[1]中的相关结果.     

一类带干扰且Cox相关的双险种风险模型

在带有随机扰动的环境中,考虑保单到达及索赔到达均为Cox点过程且两类索赔到达过程相关的一类双险种风险模型.利用鞅技巧,将破产概率的指数上界推广到了更一般的情形.     

带干扰的双二项风险模型的破产概率

首先将[3]的双二项风险模型推广到带干扰项的一种新模型,然后讨论了盈余过程的性质,并利用盈余过程的性质给出了有关破产概率的两个结论。     

具有Vasicek利率的风险过程的破产概率的分解(英文)

In this paper, it is assumed that an insurer with a jump-diffusion risk process would invest its surplus in a bond market, and the interest structure of the bond market is assumed to follow the Vasicek interest model. This paper focuses on the studying of the ruin problems in the above compounded process. In this compounded risk model, ruin may be caused by a claim or oscillation. We decompose the ruin probability for the compounded risk process into two probabilities： the probability that ruin caused by a claim and the probability that ruin caused by oscillation. Integro-differential equations for these ruin probabilities are derived. When the claim sizes are exponentially distributed, the above-mentioned integro-differential equations can be reduced into a three-order partial differential equation.     

双更新风险模型

本文讨论了具有两个到达过程的更新模型,在只要求点间间距的分布是绝对连续的简单条件下,利用鞅的乘积性质,得到了最终破产概率和有限时间破产概率的一个上界.     

带干扰的Erlang(2)过程

本篇论文主要讨论带干扰的E rlang(2)过程,首先通过指数分布的可加性来推得生存概率所满足的积分微分方程,进而得到破产概率(由干扰引起和由索赔引起)所满足的积分微分方程,最后得到破产概率的拉氏变换所满足的方程.     

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本文考虑了常利力下带干扰的双复合Poisson风险过程, 借助微分和伊藤公式, 分别获得了无限时和有限时生存概率的积分微分方程. 当保费服从指数分布时, 得到了无限时生存概率的微分方程.     

Uniform asymptotic estimates for ruin probabilities of renewal risk models with exponential Lévy process investment returns and dependent claims

This paper investigates the ruin probabilities of a renewal risk model with stochastic investment returns and dependent claim sizes. The investment is described as a portfolio of one risk‐free asset and one risky asset whose price process is an exponential Lévy process. The claim sizes are assumed to follow a one‐sided linear process with independent and identically distributed step sizes. When the step‐size distribution is heavy tailed, we establish some uniform asymptotic estimates for the ruin probabilities of this renewal risk model. Copyright © 2012 John Wiley & Sons, Ltd.     

带干扰的双Cox风险模型的破产概率

对于受布朗运动干扰的双Cox模型,用鞅方法得到了估计其破产概率上界的Lundberg不等式,并对Lundberg不等式进行了推广.     

Finite Time Ruin Probabilities and Large Deviations for Generalized Compound Binomial Risk Models

In this paper, we extend the classical compound binomial risk model to the case where the premium income process is based on a Poisson process, and is no longer a linear function. For this more realistic risk model, Lundberg type limiting results for the finite time ruin probabilities are derived. Asymptotic behavior of the tail probabilities of the claim surplus process is also investigated.     

Existence and Application of Optimal Markovian Coupling with Respect to Non-Negative Lower Semi-Continuous Functions

Abstract In this paper, for two given transition probabilities, the existence of the optimal Markovian coupling with respect to a non-negative lower semi-continuous function is proved. As an application of this result, the well-known Strassen's theorem is generalized. Moreover, it is proved that the existence of an order-preserving Markovian coupling of two given jump processes is equivalent to their stochastical comparability. Research supported in part by DPFIHE (Grant No. 96002704) and NNSFC (Grant No. 19771008)